Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

Primary students’ interpretation of maps : gesture use and mapping knowledge

Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

Stop whining and make the best of it: a cross-national comparison of response to regional disadvantage in the wine industry

Our cross-national field study of wine entrepreneurship in the “wrong” places provides some redress to the focus of the “regional advantage” literature on places that have already won and on the firms that benefit from “clusters” and other centers of industry advantage. Regional “disadvantage” is at best a shadowy afterthought to this literature. By poking around in these shadows, we help to synthesize and extend the incipient yet burgeoning literature on entrepreneurial “resourcefulness” and we contribute to the developing body of insights and theory pertinent to the numerous but often ignored firms and startups that mostly need to worry about how they will compete at all now if they are ever to have of chance of “winning” in the future. The core of our findings suggests that understandable – though contested – processes of ingenuity underlie entrepreneurial responses to regional disadvantage. Because we study entrepreneurship that from many angles simply does not make sense, we are also able to proffer a novel perspective on entrepreneurial sensemaking.

Stop whining and make the best of it : a cross-national comparison of responses to regional disadvantage in the wine industry

Our cross-national field study of wine entrepreneurship in the “wrong” places provides some redress to the focus of the “regional advantage” literature on places that have already won and on the firms that benefit from “clusters” and other centers of industry advantage. Regional “disadvantage” is at best a shadowy afterthought to this literature. By poking around in these shadows, we help to synthesize and extend the incipient yet burgeoning literature on entrepreneurial “resourcefulness” and we contribute to the developing body of insights and theory pertinent to the numerous but often ignored firms and startups that mostly need to worry about how they will compete at all now if they are ever to have of chance of “winning” in the future. The core of our findings suggests that understandable – though contested – processes of ingenuity underlie entrepreneurial responses to regional disadvantage. Because we study entrepreneurship that from many angles simply does not make sense, we are also able to proffer a novel perspective on entrepreneurial sensemaking.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

Worthless and undeserving? : problematising the subjectivities of single parenthood

A considerable body of knowledge has been constructed perpetuating the notion single parenthood is a significant problem for society, and while this is supported by specific research designs and sampling practices, it is also maintained by two key discourses. The first constitutes single parenthood as a deficit, while the second identifies it as a risk. In both cases, these discourses are operationalised by the philosophy of neo-liberalism, which envisions good citizenship as economic autonomy. Historically, it has been the convergence of the risk and deficit discourses that has constituted single parenthood as a social problem. More recently, however, risk discourses have come to dominate thinking about single parenthood. As a result, this thesis terms risk discourses as dominant discourses. As dominant discourses, risk sidelines or discounts other ways of thinking about single parenthood. While a few exceptions are notable, including some feminist, poststructural and family resilience scholars, most researchers appear unable to see past the positioning of these discourses and envision another way of being for parents who are single. This means that alternative subjectivities are obscured and have limited influence in this field of research. Because this thesis aimed to problematise dominant subjectivities of single parenthood, a poststructural Foucauldian framework has been utilized in order to document the discursive constructions of single parenthood through literature, insider discourses, and outsider discourses. For the purposes of this thesis, outsider discourses are constituted as those outside the subjectivities of single parenthood, such as media and research discourses. An examination of the Australian media has been undertaken over a one year period, the results of which form the basis for the analysis of media discourses of single parenthood. Parents who are single were also targeted for self selection into this project to provide insider discourses about single parenthood. This analysis explored how respondents negotiated the discourses of single parenthood and how they themselves used or rejected the subjectivities constructed for them via these discourses to constitute their own subjectivities. This thesis aimed to explore the role of discourses in the construction of individuals' subjectivities. Specifically, it draws attention to the way in which knowledge and power work through discourses to emphasize what is allowable, both publicly and privately, in relation to single parenthood. Most importantly, this thesis offers alternative subjectivities for single parenthood to facilitate new ways of thinking about parents who are single.

Agreement between self-reported use of in vitro fertilization or ovulation induction, and medical insurance claims in Australian women aged 28–36 years

STUDY QUESTION: What is the self-reported use of in vitro fertilization (IVF) and ovulation induction (OI) in comparison with insurance claims by Australian women aged 28–36 years? SUMMARY ANSWER: The self-reported use of IVF is quite likely to be valid; however, the use of OI is less well reported. WHAT IS KNOWN AND WHAT THIS PAPER ADDS: Population-based research often relies on the self-reported use of IVF and OI because access to medical records can be difficult and the data need to include sufficient personal identifying information for linkage to other data sources. There have been few attempts to explore the reliability of the self-reported use of IVF and OI using the linkage to medical insurance claims for either treatment. STUDY DESIGN: This prospective, population-based, longitudinal study included the cohort of women born during 1973–1978 and participating in the Australian Longitudinal Study on Women's Health (ALSWH) (n = 14247). From 1996 to 2009, participants were surveyed up to five times. PARTICIPANTS AND SETTING: Participants self-reported their use of IVF or OI in two mailed surveys when aged 28–33 and 31–36 years (n = 7280), respectively. This study links self-report survey responses and claims for treatment or medication from the universal national health insurance scheme (i.e. Medicare Australia). MAIN RESULTS AND THE ROLE OF CHANCE: Comparisons between self-reports and claims data were undertaken for all women consenting to the linkage (n = 3375). The self-reported use of IVF was compared with claims for OI for IVF (Kappa, K = 0.83), oocyte collection (K = 0.82), sperm preparation (K = 0.83), intracytoplasmic sperm injection (K = 0.40), fresh embryo transfers (K = 0.82), frozen embryo transfers (K = 0.64) and OI for IVF medication (K = 0.17). The self-reported use of OI was compared with ovulation monitoring (K = 0.52) and OI medication (K = 0.71). BIAS, CONFOUNDING AND OTHER REASONS FOR CAUTION: There is a possibility of selection bias due to the inclusion criteria for participants in this study: (1) completion of the last two surveys in a series of five and (2) consent to the linkage of their responses with Medicare data. GENERALIZABILITY TO OTHER POPULATIONS: The results are relevant to questionnaire-based research studies with infertile women in developed countries. STUDY FUNDING/COMPETING INTEREST(S): ALSWH is funded by the Australian Government Department of Health and Ageing. This research is funded by a National Health and Medical Research Council Centre of Research Excellence grant.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Effect of an adiabatic fin on natural convection heat transfer in a triangular enclosure

Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.

Development of a bi-material representative volume element using damaged homogenisation approach

Most civil engineering structures are formed using a number of materials that are bonded to each other with their surface-to-surface interaction playing key role on the overall response of the structure. Unfortunately these interactions are extremely variable; simplified and extremely detailed models trialed to date prove quite complex. Models that assume perfect interaction, on the other hand, predict unsafe behavior. In this paper a damage mechanics based interaction between two materials of different softening properties is developed using homogenisation approach. This paper describes the process of developing a bi-material representative volume element (RVE) using damaged homogenisation approach. The novelty in this paper is the development of non-local transient damage identification algorithm. Numerical examples prove the stability of the approach for a simplified RVE and encourage application to other shapes of RVEs.